Find an explicit formula for the following equence, an which tart with a1=23. 23,34,45,56,…

The equation of the parabola that passes through (0, -5) and has a vertex at (-1, 4) will be y = -9(x + 1)² + 4.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The vertex of the parabola is at (-1, 4). Then the equation is given as,

y = a(x + 1)² + 4

The equation passes through (0, -5), then we have

y = a(x + 1)² + 4

-5 = a(0 + 1)² + 4

-5 = a + 4

a = -9

Then the equation of the parabola that passes through (0, -5) and has a vertex at (-1, 4) will be y = -9(x + 1)² + 4

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Answer:

x=d

Step-by-step explanation:

The values of the expressions are x = √6, y = 2√3 and z = √2

From the question, we have the following parameters that can be used in our computation:

[tex]x =\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} }[/tex]

[tex]y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} }[/tex]

[tex]z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex]

We have

[tex]x =\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} }[/tex]

Take the square of both sides

So, we have

[tex]x^2 =12-3\sqrt{7} + 12 + 3\sqrt{7} - 2(\sqrt{12-3\sqrt{7} } * \sqrt{12 + 3\sqrt{7} })[/tex]

This gives

x² = 12 - 3√7 + 12 + 3√7 - 2√81

Evaluate the roots

So, we have

x² = 12 - 3√7 + 12 + 3√7 - 18

Evaluate the sum and the difference

x² = 6

Take the square roots of both sides

x = √6

Using the same steps above, we have

[tex]y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} }[/tex]

Square both sides

So, we have

[tex]y^2 = 7 - 4\sqrt 3 + 7 + 4\sqrt 3 - 2 * \sqrt{7-4\sqrt{3 } } * \sqrt{7 + 4\sqrt{3} }[/tex]

This gives

[tex]y^2 = 7 - 4\sqrt 3 + 7 + 4\sqrt 3 - 2 * 1[/tex]

Evaluate

y² = 12

Take the square root of both sides

y = 2√3

Lastly, we have

[tex]z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex]

Square both sides

[tex]z^2 = 2 + \sqrt 3 + 2- \sqrt 3 - 2 * \sqrt{2 + \sqrt{3} } * \sqrt{2 - \sqrt{3} }[/tex]

This gives

z² = 4 - 2 *1

Evaluate

z = √2

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Answer:

She spend $7 a month on downloads.

Step-by-step explanation:

y = the total spent on downloads

x = number of months

m = the amount spent each month

y = mx

45.50 = m(6.5)  Divide both sides by 6.5

7 = m

The required values of the compound amount are $56740.76, $56982.05, $57191.25, $57232.60 and $57234.01 respectively.

What is compound interest?

Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The main (initial) sum and the interest that has already accrued over the course of prior periods are used to calculate compound interest.

Given, Principal (P) = $42,400

interest rate(r) = 6% per year = 0.06

time(t) = 5 years

The compound amount is given by

[tex]A = P(1+\frac{r}{t} )^{nt}[/tex]

For compounded annually, n=1

[tex]A = 42400(1+0.06)^{1*5}[/tex] = $56740.76

For compounded semi-annually, n=2

[tex]A = 42400(1+\frac{0.06}{2})^{2*5}[/tex] = $56982.05

For compounded monthly, n=12

[tex]A = 42400(1+\frac{0.06}{12})^{12*5}[/tex] = $57191.25

For compounded daily, n=365

[tex]A = 42400(1+\frac{0.06}{365})^{365*5}[/tex] = $57232.60

For compounded continuously,

[tex]A=Pe^{rt} = 42400e^{0.06*5}[/tex] = $57234.01

Hence, these are the required values of the compound amount.

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Answer:

multiple

Step-by-step explanation:

I had the same question and guessed and that was the answer lol

Answer:

B: 3(x-6) = 3x-18

Step-by-step explanation:

The left and right sides of this equation are actually equal! We can see this by dividing the 3 on the left through the parentheses. This gives us [tex]3x-18[/tex], which is equal to the right-hand side of the equation!

To solidify this, we add 18 to both sides, and subtract 3x from both sides, which gives us that 0=0, so there are infinitely many solutions for x(since no matter what x is, it will result in 0=0 which is always true).

I hope this helps!

The equation of the new function is: f(x) = (x- 3)²

Function is a type of relation, or rule, that maps one input to specific single output.

The translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

We know that the function f(x+m) is equals to the function f(x) translated 'm' times to the left.

Therefore, to find the translate the function f(x) = x² twelve units to the right, we have given;

f(x- 3) = (x- 3)²

Therefore, the new function is: f(x) = (x- 3)²

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He has a total of $90 in his cafeteria wallet, thus the most lunches he may purchase is 20.

A number is divided in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that can be made. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

Here,

Amount added=$50

Amount already in wallet=$40

Total amount in wallet=50+40

=$90

Cost of each lunch=$4.5

Number of lunch he can buy,

=90/4.5

=20

The maximum number of lunch he can buy is 20 lunch as he has a total of $90 in his cafeteria wallet.

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Answer:

18x^2 + 9x - 20

18x^2 + 24x - 15x - 20

6x(3x+4) - 5(3x+4)

Therefore, (6x-5)(3x+4)

The constant that must be added to both sides of the equation to find the perfect square is b/2a.

The 2nd equation in x is known as a quadratic function. Ax2 + Bx + c = 0 is the quadratic equation in standard form, wherein there a and b are the coefficient, x is the constant, and c is the constant.

The presence of a non-zero component in the coefficient of x2 (a ≠ 0) is the first prerequisite for an expression to be a quadratic equation.

As per the given information in the question,

The equation for the quadratic equation is,

Ax² + Bx + c = 0

And for finding the roots,

d = b² - 4ac

Then, use the formula (-b±√d)/2a.

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An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

1 pound = $1.38

175 pounds = $241.50

The number of pounds for the strawberries order of $241.50 is

175 pounds.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cost of strawberries per pound = $1.38

The cost of a strawberry order = $241.50

The number of pounds for the order of $241.50.

1 pound = $1.38

Multiply 241.50/1.38 on both sides.

241.50/1.38 x 1 pound = $241.50

175 pounds = $241.50

Thus,

The number of pounds for the strawberries order of $241.50 is

175 pounds.

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The complete question is:

A grocer can buy strawberries for $1.38 per pound.

Write an equation relating c, the cost, and p, the pounds of strawberries.

A strawberry order cost $241.50.

How many pounds did the grocer order?

The lines C and D are parallel.

What is a line?

In pure mathematics, a line is an infinitely long object with no dimension, depth, or curvature. Thus, lines ar one-dimensional objects, although they'll exist in 2, three, or higher dimension areas

Main body:

As Line LM cuts the line at C the angle made by both line is 48°

and line NP cuts the line at D , the angle made by line is 132°

we know that to make a line parallel , the sum of angle on one side of the line should be 180°

∠C +∠D = 48° +132°

             = 180°

Hence , the lines C and D are parallel.

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Answer:

g(x)=3^x+7

Step-by-step explanation:

f(0)=3^0

that is the y-intercept

now we can take the known y-intercept of g(x) which is 8 and then we can get our b in the y=mx+b equation.

Answer:

4 916 083

Step-by-step explanation:

population in 1990

1.5 : 100 = x : 4 786 000

x = 1.5 · 4 786 000 / 100

x = 1.5 · 47 860

x = 71 790

4 786 000 + 71 790 = 4 857 790

population in 2000

1.2 : 100 = x : 4 857 790

x = 1.2 · 4 857 790 / 100

x = 0.012 · 4 857 790

x = 58 293.48

4 857 790 + 58 293.48 = 4 916 083.48

The subtraction of significant figures between the distance is 5.01 × 10⁷km

In this problem, we have to subtract the difference between the distance of Venus and Mercury. When subtracting significant digits, the amount of significant digits that will be in the final answer is determined by the number of significant digits present after the decimal place in the numbers we are subtracting.

The distance between Venus and Mercury can be calculated as

1.08 × 10⁸ - 5.79 × 10⁷ = 50,100,000km

To express the value in significant figures, we will have

50,100,000 = 5.01 × 10⁷km

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The 4th proportional of the given ratio is 4/3. option C

The range of the data 112, 121, 184, 189, 177, 190 is 78. option A

It follows from the concept of proportions that the ratios can be represented as follows;

21 : 7 = 4 : 3a + 1

21/7 = 4 / (3a + 1)

cross product

21 × (3a + 1) = 4 × 7

63a + 21 = 28

subtract 21 from both sides

63a = 28 - 21

63a = 7

a = 7/63

a = 1/9

So,

3a + 1

= 3(1/9) + 1

= 3/9 + 1

= 1/3 + 1

= 1 ⅓

= 4/3

21 : 7 = 4 : 4/3

Range of the data:

112, 121, 184, 189, 177, 190

Recall, the range of a dataset is the difference between the maximum and minimum data values and hence, we have;

Range = Highest data value - Lowest data value

= 190 - 112

= 78

Therefore, the range of the given set of data is 78.

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Answer:

The surface area of cube = 6 side2

According to the question,

Let the side of the cube be x

Each side of the cube increased by 50%.

= x(100 + 50)/100 = 1.5x

The surface area of the cube

⇒6x²

The new surface area of the cube (side = 1.5x)

⇒ 6 × 2.25x²

Increase percentage in the surface area

⇒((6 x 2.25 x²-6x²)/6 x² }× 100

⇒ 125%

80, 7, and 2.87 are not irrational numbers.

What is an irrational number?

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0. Example: √2, √3, √5, etc all are irrational.

Given numbers: 80, 7, 2.87, √59

80 = It is a rational number

7 = It is a rational number

2.87 = It is a rational number

√59 = It is an irrational number.

Hence, 80, 7, and 2.87 are not irrational numbers.

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The equation is 2w + 10 = 26.

The number of weeks the driving class lasts is 8 weeks.

With that,

Terrence signed up for the Safe Venture driving school.

He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes.

When Terrence completes the 26 total hours of instruction, he will take his driver's test.

We have to determine,

Which equation can you use to find w, the number of weeks the driving class lasts.

According to the question,

He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes.

Then, The equation of the number of weeks the driving class lasts,

= 2w + 10

When Terrence completes the 26 total hours of instruction, he will take his driver's test.

2w + 10 = 26

He spends 10 hours driving and adding on 2 more classes with a total of 26 hours.

Therefore,

The number of weeks the driving class lasts,

2W + 10 = 26

2W = 26 - 10

2W = 16

W = (16/2)

W = 8

Hence, The number of weeks the driving class lasts is 8 weeks.

The exterior angle to ∠X is 104.25°

The exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle. The theorem can be used to find the measure of an unknown angle in a triangle.

from the above definition , if ∠Y = 62.45° and ∠Z = 41.8°

It means from exterior angle theorem that

exterior ∠X = ∠Y + ∠Z

exterior ∠X  = 62.45° + 41.8°

exterior ∠X  = 104.25°

In conclusion the exterior angle X is 104.25°

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The solution of the given quadratic equation is x = 1.37, - 1.37.

What is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                            The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions .

Given quadratic equation:

9x² = 17

⇒ x² = (17 / 9)

⇒ x = ± √(17 / 9)

⇒ x = ± (√17) / 3

⇒ x = 1.37, - 1.37

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Answer: 20

Step-by-step explanation:

Using the side splitter theorem yields:

[tex]\frac{?}{5}=\frac{12}{3}\\\\\frac{?}{5}=4\\\\?=20[/tex]

Answer:

20

Step-by-step explanation:

the scale factor from the little triangle to the larger triangle is 5/4

[tex]\frac{5x}{4}[/tex] = x + 5  Multiple through by 4 to clear the fraction

5x = 4x + 20  Subtract 4x from both sides

x = 20

The required polynomial function is f(x) = (x + i)² which is degree 2 with the zeros x = √2 and x = -i.

We have to determine a polynomial function for each set of zeros:

x = √2, -i

To write a polynomial function with the zeros x = √2 and x = -i, we can start by setting the function equal to zero and substituting in the zeros:

f(√2) = 0

f(-i) = 0

We can then solve for the coefficients by expressing the polynomial function in terms of (x - √2) and (x + i).

For example, we can write:

f(x) = (x - √2)(x + i)q(x)

for some polynomial q(x).

Substituting in the zeros, we get:

f(√2) = (√2 - √2)(√2 + i)q(√2) = 0

f(-i) = (-i - √2)(-i + i)q(-i) = 0

Solving for q(x), we find:

q(x) = (x + i)/(x - √2)

Substituting this back into the original equation, we get:

f(x) = (x - √2)(x + i)(x + i)/(x - √2)

f(x) = (x + i)²

This is a polynomial function of degree 2 with the zeros x = √2 and x = -i.

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To dig the pool, he rents a small backhoe for $95.50 a day. If his total bill comes to $286.50, for  3 days does he rent the backhoe.

What is backhoe?

A backhoe, also known as a rear actor or back actor, is a type of digging apparatus, often known as a digger, that has a digging bucket attached to the end of a two-part articulated arm. Usually, it is attached to the rear of a tractor or front loader, the latter of which is known as a "backhoe loader."

$286.50/$95.50= 3

Henry is building an in-ground pool at his house. He is doing most of the work himself to save money. To dig the pool, he rents a small backhoe for $95.50 a day. If his total bill comes to $286.50, for 3 days does he rent the backhoe.

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The required value of the x₂ is given as -0.500000.

Given that,
xₙ₊₁ = [[xₙ]³ - 1]/4, x₁ = -1

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
xₙ₊₁ = [[xₙ]³ - 1]/4, x₁ = -1
put n = 2
x₂ = [[x₁]³ - 1]/4
    =  -1 - 1 /4
    = -2/4
    = -1/2 = 0.500000

Thus, the required value of the x₂ is given as -0.500000.

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Answer:

39.05 miles

Step-by-step explanation:

0.05+0.1+38

Answer:

2.4.6.8.10

Step-by-step explanation:

that's the answer

Answer:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Step-by-step explanation:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, multiply all numbers frmo 1 to 10

Answer:

A.  1,500

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7cm}\underline{Sum of the first n terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\ \phantom{ww}$\bullet$ $n$ is the $n$th term.\\\end{minipage}}[/tex]

The given scenario can be modelled as a geometric series.

If Marcus' goal is to sell 15,000 t-shirts during the first 6 months, then:

If he projects that the number of t-shirts he sells will increase by 20% each month then the common ratio is:

Substitute these values into the formula and solve for a:

[tex]\implies 15000=\dfrac{a(1-1.2^6)}{1-1.2}[/tex]

[tex]\implies 15000(1-1.2)=a(1-1.2^6)[/tex]

[tex]\implies a=\dfrac{15000(1-1.2)}{1-1.2^6}[/tex]

[tex]\implies a=1510.586188[/tex]

Therefore, the approximate number of T-shirts Marcus needs to sell during the first month to meet his goal is 1,500.

Check:

Total = 1511 + 1813 + 2176 + 2611 + 3133 + 3760 = 15004

Check:

Total = 1500 + 1800 + 2160 + 2592 + 3110 + 3732 = 14894 ≈ 15000

The probability that both hats are different colors is; 0.7425  

We are given;

Total number of hats = 30 hats

Number of green hats = 5 hats

Number of blue hats = 7 hats

Number of red hats = 12 hats

Number of brown hats = 6 hats

Now, if Mary selects two hats at random, then the probability that they are different colors is;

P(they are different colors) = 1 - P(both are the same color)

P(both are the same color) = (⁵/₃₀ * ⁴/₂₉) + (⁷/₃₀ * ⁶/₂₉) + (¹²/₃₀ * ¹¹/₂₉) + ( ⁶/₃₀ * ⁵/₂₉)

= (20 + 42 + 132 + 30)/(30*29)

=  224/(30*29)

= 0.2575

Thus;

P(they are different colors) = 1 - 0.2575

P(they are different colors) = 0.7425  

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